Question

this is the graph of $y = \log_2(x + 4)$. complete the sentence to describe the functions domain and range. the functions domain is and the range is

Explanation:

Step1: Find the domain

For the function \(y = \log_{2}(x + 4)\), the argument of the logarithm \(x+4>0\).
Solving \(x + 4>0\) gives \(x>-4\).

Step2: Find the range

The range of a logarithmic function \(y=\log_{a}(u)\) (where \(a>0,a
eq1\)) is all real numbers. Since the function \(y = \log_{2}(x + 4)\) is a transformation (horizontal shift) of the basic logarithmic function \(y=\log_{2}(x)\), its range remains unchanged.

Answer:

The function's domain is \(x>-4\) (or \((-4,\infty)\)) and the range is all real numbers (or \((-\infty,\infty)\)).